Avia dicit amicitiam bonam vitam laetiorem facere.

Because after dicit, Latin is using an indirect statement.

In this construction:

• the verb of the reported statement goes into the infinitive
• the subject of that infinitive goes into the accusative

So the direct statement would be:

• Amicitia bona vitam laetiorem facit

But after dicit, it becomes:

• amicitiam bonam vitam laetiorem facere

That is a very common Latin pattern after verbs like say, think, know, hear, and believe.

There are two different subjects, one for each verbal idea:

• Avia is the subject of dicit
• amicitiam bonam is the subject of facere

So avia is the one doing the saying, but amicitiam bonam is the thing that is said to make life happier.

This is one of the big things to get used to in Latin indirect statement: the subject of the infinitive is often not nominative.

Because in an indirect statement, the subject of the infinitive is put in the accusative, not the nominative.

So:

• direct statement: amicitia bona
• indirect statement after dicit: amicitiam bonam

Even though amicitiam bonam is logically the subject of facere, grammatically Latin puts it in the accusative because of the construction.

Because vitam is the direct object of facere.

In the direct version:

• Amicitia bona vitam laetiorem facit

vitam is already accusative there, because friendship makes life ...

When the sentence becomes indirect, vitam stays accusative for the same reason: it is still the object of facere.

So the two accusatives are doing different jobs:

• amicitiam bonam = subject of the infinitive
• vitam = object of the infinitive

Laetiorem agrees with vitam.

They go together because Latin often uses:

• object + predicate adjective after verbs like facere

So vitam laetiorem facere means:

• to make life happier

Here:

• vitam = the thing being affected
• laetiorem = the resulting state of that thing

This is often called a predicate accusative or an object complement.

Because laetiorem is a comparative adjective, and comparatives in Latin use third-declension endings.

The positive adjective is:

• laetus, laeta, laetum = happy

But the comparative is:

• laetior for masculine/feminine
• laetius for neuter

So the accusative singular masculine/feminine form is:

• laetiorem

That is why it does not look like bonam.
Bonam is an ordinary first/second-declension adjective form, while laetiorem is a comparative form.

This is a very good question, because by endings alone bonam could match either noun: both amicitiam and vitam are feminine accusative singular.

What tells us the intended meaning is mainly:

• word grouping: amicitiam bonam naturally stays together
• sentence structure: vitam laetiorem facere is a standard pattern meaning make life happier
• sense/context: the intended meaning is good friendship, not good life

So this is one of those places where Latin can be briefly ambiguous if you look only at endings. In real reading, structure and meaning usually resolve it.

It would be:

• Amicitia bona vitam laetiorem facit.

That version is helpful because it shows the underlying sentence more clearly.

Compare the two:

• Amicitia bona → becomes amicitiam bonam
• facit → becomes facere

But vitam laetiorem stays the same, because it is still the object plus its complement.

Yes, in English you would often translate with that:

• Grandmother says that ...

But Latin usually does not use a separate word for that in this construction. Instead, the idea of that is built into the accusative + infinitive pattern.

So dicit amicitiam bonam vitam laetiorem facere means says that good friendship makes life happier.

Because a comparative adjective in Latin does not always have to state the second thing being compared.

So laetiorem can simply mean:

• happier
• more happy

The comparison is understood from the idea itself: life becomes happier than it was before, or happier than it would otherwise be.

English works the same way:

• Friendship makes life happier

We do not have to add than before, even though that idea is understood.

Yes. Latin word order is much freer than English word order because the endings show the grammatical roles.

For example, Latin could move things around for emphasis. But not every arrangement is equally clear or natural. A writer will often keep related words near each other, as here:

• amicitiam bonam
• vitam laetiorem

That makes the sentence easier to follow.

So word order in Latin is flexible, but it is still meaningful: it can help show emphasis, grouping, and style.